Boundary element methods such as displacement discontinuity method (DDM) are promising for describing the geo-mechanics of growing fractures as they reduce the dimensionality of the problem by one. Still, this advantage is overshadowed by the computational power required to model stage scale simulations of hydraulic fractures primarily due to nonlinearity arising from the fluid flow inside the fracture. Typical assumptions of DDM based models to improve computational efficiency lead to their inability to describe proppant transport which is critical to treatment design.

We developed a new algorithm for faster solution of fully-coupled problem of geomechanics described using DDM and fluid flow in the fracture. The algorithm employs an analytical, local linear approximation of the Reynolds lubrication equation to estimate an initial guess of the solution. The guessed solution is then refined by solving the coupled non-linear system using fixed-point iteration method. The fluid inside the fracture is modeled as a slurry and captures the effect of proppant distribution and fluid rheology (non-Newtonian flow).

The implementation of the new algorithm reduces the total number of iterations for solution by an order of magnitude. This improvement has allowed us to use the algorithm to develop a fully-coupled, three- dimensional hydraulic fracturing simulator which can run in an acceptable runtime without the need for high-performance computing. The simulator captures the effect of proppant transport, rheology of fluid, leak-off, natural fractures, and hydraulic fractures from previous stages on fracture growth. The new algorithm allows us to conveniently model multiple growing fractures of varying height and capture the interaction between them (stress-shadow). The simulator is validated against conventional fracture propagation models (PKN and KGD). Simulated results show excellent agreement with the analytical solution. We present results of stage scale simulations run using the new simulator that demonstrate the effect of compressional stresses due to stress shadow on proppant distribution in the fracture.

The algorithm presented here provides a new efficient approach for solving coupled fluid flow and geomechanics (DDM) problem. It has the benefit of reduced simulation time and increased stability. The developed simulator can predict final propped fracture area and account for effects from previous stages. It can serve as an excellent tool for designing hydraulic fracturing treatments.